GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 03:34 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Within a rectangular courtyard of length 60 feet, a graveled path,

Author Message
TAGS:

### Hide Tags

Intern  Joined: 25 Aug 2018
Posts: 2
Within a rectangular courtyard of length 60 feet, a graveled path,  [#permalink]

### Show Tags

1 00:00

Difficulty:   65% (hard)

Question Stats: 50% (03:24) correct 50% (03:42) wrong based on 23 sessions

### HideShow timer Statistics

Within a rectangular courtyard of length 60 feet, a graveled path, 3 feet wide, is laid down along all the four sides. The cost of graveling the path is Rs 2 per sqft. If the path had been twice as wide, the gravek would have cost Rs 984 more. The width of the courtyard is :

A 24
B 30
C 40
D 45
E 54
Intern  B
Joined: 14 Feb 2018
Posts: 6
Within a rectangular courtyard of length 60 feet, a graveled path,  [#permalink]

### Show Tags

Being x the width of the rectangle, we have the following equation:

$$2[2(60*3)+2*3(x-6)] + 984 = 2[2(60*6)+2*6(x-12)]$$

where $$2(60*3)$$ is the area of the path next to the longer side (60 ft long and 3 ft wide), and $$2*3(x-6)$$ the area of the path next to the shorter side, avoiding to count the area from the corner twice. Then we need to repeat the same idea with the bigger path. Both areas are multiplied by 2 because we are measuring the cost, which is Rs 2 per sq ft. We have to consider that the path with double size is Rs 984 more expensive, so we add this into our equation. Then, we can solve the equation:

$$2[360+6x-36]+984=2(720+12x-144)$$
$$360+6x-36+492=720+12x-144$$
$$324+6x+492=576+12x$$
$$816-576=6x$$
$$240=6x$$
$$x=40$$

Thus, C is the correct answer.
Manager  G
Joined: 02 Aug 2015
Posts: 153
Re: Within a rectangular courtyard of length 60 feet, a graveled path,  [#permalink]

### Show Tags

sultanatehere wrote:
Within a rectangular courtyard of length 60 feet, a graveled path, 3 feet wide, is laid down along all the four sides. The cost of graveling the path is Rs 2 per sqft. If the path had been twice as wide, the gravek would have cost Rs 984 more. The width of the courtyard is :

A 24
B 30
C 40
D 45
E 54

A = Area of outer rectangle = 60 x Width
Ax = Area of inner rectangle with width of 3 = 54 x (Width-6)
Ay = Area of inner rectangle with twice the width, i.e 6 = 48 x (Width - 12)

Area of gravel with normal width = A-Ax
Area of gravel with twice width = A-Ay

Given, cost of gravelling twice width - cost of gravelling normal width = 984.
Given, cost of gravelling = Rs2/sq ft.

2(A-Ay) - 2(A-Ax) = 984.
A-Ay-A+Ax=492.
Ax-Ay=492.

On substituting Ax and Ay from above and solving the above equation, we get width=40.

Hence C.

Cheers!
Manager  S
Joined: 21 Jul 2018
Posts: 185
Re: Within a rectangular courtyard of length 60 feet, a graveled path,  [#permalink]

### Show Tags

Tried to solve using an Ans choices and got lucky with the 1st option Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: Within a rectangular courtyard of length 60 feet, a graveled path,  [#permalink]

### Show Tags

sultanatehere wrote:
Within a rectangular courtyard of length 60 feet, a graveled path, 3 feet wide, is laid down along all the four sides. The cost of graveling the path is Rs 2 per sqft. If the path had been twice as wide, the gravek would have cost Rs 984 more. The width of the courtyard is :

A 24
B 30
C 40
D 45
E 54

We can let w = the width of the courtyard. Therefore, the courtyard, including the graveled path, has an area of 60w sq ft. Excluding the path, the area of the courtyard would be (60 - 2(3))(w - 2(3)) = 54(w - 6) = 54w - 324 sq ft. So the path alone has an area of 60w - (54w - 324) = 6w + 324 sq ft. Since the cost of graveling the path is Rs 2 per sq ft, the cost of graveling the path is Rs 12w + 648.

If the path had been twice as wide, then the courtyard, including the path, would still have an area of 60w sq ft. However, excluding the path, the area of the courtyard would be (60 - 2(6))(w - 2(6)) = 48(w - 12) = 48w - 576 sq ft. So the path alone would have an area of 60w - (48w - 576) = 12w + 576 sq ft, and the cost of the path would be Rs 24w + 1152. We are told that this would cost Rs 984 more, so we can set up the following equation to solve for w:

12w + 648 + 984 = 24w + 1152

12w + 1632 = 24w + 1152

480 = 12w

40 = w

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Within a rectangular courtyard of length 60 feet, a graveled path,   [#permalink] 27 Sep 2018, 17:20
Display posts from previous: Sort by

# Within a rectangular courtyard of length 60 feet, a graveled path,  